The present invention relates to the field of multi-symbol modulation symbol-dependent error probability levels in symbol transmission over noisy physical channels. In particular, the present invention relates to the field of cellular communications employing phase shift keying mechanisms for modulation/demodulation.
The widespread use of Internet Protocol (IP) based services and in particular Transmission Control Protocol (TCP) based services is characteristic for data communication within today's Internet. Efforts are under development to migrate those services available over the Internet to wireless networks and especially to the third generation wireless networks being currently introduced into mass market. Network operators and service providers operating in the field of third generation wireless networks hope for benefiting from the high data rate packet services operable with the third generation wireless networks in that services available up to now wire-based only might be migrated to wireless networks presenting itself to new economic opportunities. Typical applications, which benefit from high data rates, include video-clips, multimedia, e-email, telematics, gaming, video-streaming etc.
High Speed Downlink Packet Access (HS-DPA) has been developed and standardized in the context of the Third Generation Partnership Project (3GPP) and in particular for UTRA (UMTS terrestrial radio access) FDD (frequency duplex division) domain. Besides the downlink transmission rate, which addresses the usage of a UMTS communication enabled terminals to download huge amounts of data content in a reasonable period of time, numerous network-based applications, especially data serving applications, demand for enhanced uplink data transmission rates. The typical asymmetric data transmission rates including high downlink data rates and low uplink data rates limit unnecessarily the usability of UMTS communication enabled terminals. The expected development of the hardware capabilities of mobile terminals drive the desire of user to take advantage of complex applications exchanging greater amounts of data, which implies the provision of desirably symmetric high data transmission rates or at least improved uplink data transmission rates exceeding those uplink data transmission rates available today.
Consequently, the development of a corresponding uplink packet access with enhanced uplink data rates has been provoked and is still pushed ahead in the context of the Third Generation Partnership Project (3GPP) and in particular for UTRA (UMTS terrestrial radio access) FDD (frequency duplex division) domain. In general, the enhanced uplink packet access (EUPA) under development addresses Wideband Code Division Multiple Access (WCDMA) transmission methodology. One main component to enable enhanced uplink packet access relates to the signal modulation technology employed for data signal modulation onto a physical data frequency carrier. Currently, phase shift keying (PSK) modulation and in particular 8-level phase shift key modulation (8-PSK) is under consideration.
In principle, modulation techniques are used to embed a signal (discrete or continuous) onto a carrier wave having a distinct frequency for transmission. Basically, different modulation techniques are distinguished comprising in general amplitude modulation, frequency modulation, and phase modulation. In the context of amplitude modulation (AM), the amplitude of the carrier wave is varied (modulated) in accordance with the signal to be embedded. Correspondingly, in the context of frequency modulation (FM), the frequency of the carrier wave is varied (modulated) in accordance with the signal and further, in the context of phase modulation, the phase angle of the carrier wave is varied (modulated) in accordance with the signal. It shall be noted that phase modulation (PM) can be regarded as a special case of frequency modulation (FM), where the carrier wave modulation is the time derivative of the PM modulating signal.
One specific phase modulation technique is the 8-level or 8-array phase keying modulation. With reference to FIG. 1a, a constellation diagram of 8-PSK Q-I/code modulation is schematically illustrated. 8-PSK modulation technique is a well known modulation scheme, which is for example employed in the context of EDGE standardization. The simplest form of PSK involves a 180° phase change at every transition from 0 to 1 or vice versa in an incoming bit stream. With 8-PSK modulation technique the incoming bit stream can be treated in groups of 3 bits at a time and allows coding and transmission of 8 different symbols, each of which consists of a pre-defined 3 bit sequence. Each 8-PSK symbol corresponds to a variation of the phase angle about π/4, illustratively depicted by 8-PSK symbols at angles φi[rad]=π/8+i·π/4 (and φi[deg]=22.5°+i·45°, respectively), where i=0, 1, . . . , 7. Each 8-PSK symbol is assigned to a pre-defined 3-bit group depicted in FIG. 1a. This means, the 8-PSK symbol at the different phase angles φi[rad] are associated with the 3-bit group {s0,s1,s2} in accordance with following table:
φi[rad]{s0,s1,s2} π/8{0,0,0} {circumflex over (=)} 000 3π/8{0,0,1} {circumflex over (=)} 001 5π/8{0,1,1} {circumflex over (=)} 011 7π/8{0,1,0} {circumflex over (=)} 010 9π/8{1,1,0} {circumflex over (=)} 11011π/8{1,1,1} {circumflex over (=)} 11113π/8{1,0,1} {circumflex over (=)} 10115π/8{1,0,0} {circumflex over (=)} 100
Those skilled in the art will appreciate that the higher band width efficiency and improved link level performance gained by the 8-PSK is achieved at the costs of a reduced noise resistance. Because of the fact that the states in 8-PSK are quite close together, the amount of noise required for errors to occur can be relatively small—certainly smaller than the amount of noise that Gaussian Minimum Shift Keying (GMSK) can handle, where GMSK is the standard modulation used by GSM.
With reference to FIG. 1b, soft bit level decisions are illustrated which enable a receiver to reconstruct the 3-bit groups from 8-PSK symbols received. Several soft bit level decisions are applicable for transforming 8-PSK symbols into 3-bit groups each having three bits. One possible soft bit level decisions can be defined mathematically as following:
            {                        s          ⁢                                          ⁢          0                ,                  s          ⁢                                          ⁢          1                ,                  s          ⁢                                          ⁢          2                    }        =                            {                                                                      s                  ⁢                                                                          ⁢                  0                                                                                                      s                  ⁢                                                                          ⁢                  1                                                                                                      s                  ⁢                                                                          ⁢                  2                                                              }                T            =                        {                                                                                          s                    ⁢                                                                                  ⁢                    0                                    =                                      {                                                                                                                        0                            ,                                                                                          if                                ⁢                                                                                                                                  ⁢                                Im                                ⁢                                                                  {                                  z                                  }                                                                                            >                              0                                                                                                                                                                                                        1                            ,                                                                                          if                                ⁢                                                                                                                                                                          ⁢                                                                                                                                                                        ⁢                                Im                                ⁢                                                                  {                                  z                                  }                                                                                            <                              0                                                                                                                                                                                                                                                                    s                    ⁢                                                                                  ⁢                    1                                    =                                      {                                                                                                                        0                            ,                                                                                          if                                ⁢                                                                                                                                  ⁢                                Re                                ⁢                                                                  {                                  z                                  }                                                                                            >                              0                                                                                                                                                                                                        1                            ,                                                                                          if                                ⁢                                                                                                                                  ⁢                                Re                                ⁢                                                                  {                                  z                                  }                                                                                            <                              0                                                                                                                                                                                                                                                                    s                    ⁢                                                                                  ⁢                    2                                    =                                      {                                                                                                                        0                            ,                                                                                                                            if                                  ⁢                                                                                                                                                Re                                      ⁢                                                                              {                                        z                                        }                                                                                                                                                                                                                -                                                                                                                                        Im                                    ⁢                                                                          {                                      z                                      }                                                                                                                                                                                                    >                              0                                                                                                                                                                                                        1                            ,                                                                                                                            if                                  ⁢                                                                                                                                                Re                                      ⁢                                                                              {                                        z                                        }                                                                                                                                                                                                                -                                                                                                                                        Im                                    ⁢                                                                          {                                      z                                      }                                                                                                                                                                                                    <                              0                                                                                                                                                                                                        }                T              ,where {s0,s1,s2} represents a bit vector mapped to a 8-PSK symbol, where s0 shall be assumed as the most significant bit and s2 shall be assumed as the less significant bit of the 3-bit group obtainable from the bit vector. The soft bit level decisions are illustrated correspondingly in the diagrams of FIG. 1b, which include exemplary a symbol vector z referring to the 8-PSK symbol φi[rad]=3π/8 and the 3-bit group 001{circumflex over (=)}{0,0,1}. The complex plane, in which the 8-PSK symbol vector z is illustrated, is divided by each soft bit level decision into two half-planes. This means, the value of the soft bits sj (j=0, 1, 2) are obtainable by identifying the half-plane in which the 8-PSK symbol vector z lies. Herein the 8-PSK symbol vector z lies in the half plane Im{Z}>0, Re{z}>0, and |Re{z]|−|Im{z}<0, resulting consequently in a 3-bit group 001.
As aforementioned, the 8-PSK suffers at an increased sensitivity to noise. More seriously, the three soft bit decisions required for reconstruction 3-bit groups from 8-PSK symbols have different error possibilities. This means, the error possibilities of the bits within a 3-bit group are unbalanced. Without going into detailed theoretical considerations, it can be found that if the 8 PSK symbol φi[rad]=3π/8{circumflex over (=)}{0,0,1} is transmitted, s1 and s2 have the same higher level of error possibility in comparison with s0, which has the lower level of error possibility. With reference to the 8-PSK symbol φi[rad]=π/8{circumflex over (=)}{0,0,0} it can be derived that s0 and s2 have the higher error possibility level in comparison with s1, which has the lower error possibility level. In general, it can be conducted that s2 has always the higher level of error possibility and, in dependence on the value of s2, one of both s0 and s1 has the higher level and the other one has the lower level of error possibility. Assuming that the values of s2 are equal-distributed (each having a probability of 0.5), the probability of a higher or lower level of error probability is also equal-distributed for both s0 and s1.
Consequently, the error possibilities of the bits within a 3-bit group are unbalanced, which causes effectively in an unreliable radio frequency transmission channel a reduced overall transmission rate counteracting the higher band width efficiency and improved link level performance originally aimed by the employment of 8-PSK modulation scheme.